When modelling the epidemic using a marked Hawkes process, it is easy to consider more individual inhomogeneities, such as community structure (e.g. household) and location, immunization status against the disease, and medical conditions. This type of modelling reveals the dynamics of the epidemic, including who infected whom, which is challenging because of invisible transmission pathways [1]}, [2]}. Future work also considers the inference of ascertainment rate, using various transition kernels for modelling the latent and the reported infection cases, as well as more sophisticated ways for initializing the set of infectious triggering the epidemic process,\(\mathcal {H}_{0a}\)  and the number of susceptibles at the beginning of the process, \(S_{T_0a}\) , for each age group \(a \in \mathcal {A}\) .
